In this work, we have shown that the fan-crossing free graphs are
incomparable with the fan-crossing, 2-planar, and 1-gap-planar
graphs, respectively. There were not listed in the table of
relationships in
[1]}. It remains to show that there are
fan-crossing free graphs that are not quasi-planar graphs. Moreover,
we have added fan-crossing free graphs to the list of beyond-planar
graph classes with an NP-complete recognition problem, which was
open so far [1]}.
